A remark on continued fractions for permutations and D-permutations with a weight $-1$ per cycle
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914760066334720 |
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| author | Deb, Bishal Sokal, Alan D. |
| author_facet | Deb, Bishal Sokal, Alan D. |
| contents | We show that very simple continued fractions can be obtained for the ordinary generating functions enumerating permutations or D-permutations with a large number of independent statistics, when each cycle is given a weight $-1$. The proof is based on a simple lemma relating the number of cycles modulo 2 to the numbers of fixed points, cycle peaks (or cycle valleys), and crossings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11500 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A remark on continued fractions for permutations and D-permutations with a weight $-1$ per cycle Deb, Bishal Sokal, Alan D. Combinatorics 05A19 (Primary), 05A05, 05A15, 05A30, 30B70 (Secondary) We show that very simple continued fractions can be obtained for the ordinary generating functions enumerating permutations or D-permutations with a large number of independent statistics, when each cycle is given a weight $-1$. The proof is based on a simple lemma relating the number of cycles modulo 2 to the numbers of fixed points, cycle peaks (or cycle valleys), and crossings. |
| title | A remark on continued fractions for permutations and D-permutations with a weight $-1$ per cycle |
| topic | Combinatorics 05A19 (Primary), 05A05, 05A15, 05A30, 30B70 (Secondary) |
| url | https://arxiv.org/abs/2306.11500 |